You'd also land your lobbyist in jail pretty quick. I'm fairly certain it's more than a little illegal (on the order of treason) to accept foreign money to influence congress.
Yeah, this isn't true. It just means the lobbyist would have to register as a foreign agent lobbyist if it was lobbying on behalf of a foreign interest. It's totally legal to accept foreign money to influence congress. And as a result of citizens united, they can even run ads in support of candidates and campaigns. China too, is a person with a first amendment right!
You could, but don't be too successful or its off with your head when political winds shift. Isreal has subconscious influence over this country. You might have heard the words "holy" and Isreal in a song played in the US in December... 50 million times and delivered as sermons in churches on every street corner in the US.